If we have some complete basis where the basis functions have a finite bandwidth in fourier space, and we are interested in reproducing a function with a finite bandwidth, we know that there is some subset of our complete basis that will be enough to reproduce said function.
Is there a name for this concept? or some literature I can search for more information?
I'm specifically interested in what happens when your basis functions don't have finite extent, but exponentially decreasing extent, and how I can use this concept to talk about "minimal basis sets" to approximate some function (and the bandwidth of that function.